Simple kinematics problem — falling from a geostationary satellite

[AlternativePhysics]

Homework Statement

Given that gravitational acceleration at geostationary altitude is 0.221 m/s², and neglecting air resistance, how long does it take for a marble released from a geostationary satellite in orbit to reach the ground?

Relevant Equations

F = mg, where g varies with altitude: g(r) = GM/r²
F = mg, where g varies with altitude: g(r) = GM/r²
Orbital velocity: v = √(GM/r)

I know g at that altitude is 0.221 m/s² but I'm not sure how to integrate the increasing gravitational acceleration as the object approaches Earth. I attempted using kinematic equations but g is not constant during the fall.

 

[anuttarasammyak]

How about integrating
$$dt=\frac{dr}{v}$$
where
$$\frac{v^2}{2}-\frac{GM}{r}=const.$$?

 

[berkeman]

Welcome to PF.

how long does it take for a marble released from a geostationary satellite in orbit to reach the ground?

That's a trick question. If you release a marble from a geostationary satellite, it just continues in the same orbit as the satellite. If you mean "a marble is released from rest as a geostationary satellite goes by...", that is a different question. Did you quote the schoolwork question word-for-word?